2.1. Test data

The test cases were selected from the CASP14 website (https://predictioncenter.org/casp14/index.cgi) and mostly represent a particular type of crystal structure, namely those that have a single protein sequence in the asymmetric unit (AU) and consist of one or a few domains where the domain is unrelated, or poorly related, to known structures, making them challenging for MR. In total, 13 crystal datasets corresponding to a total of 43 predicted models were chosen based on different modeling difficulty, including free modeling (FM), hard template-based modeling (TBM-hard), and the boundary between FM and TBM (FM/TBM). As shown in Table 1, the resolution ranged from 1.5 to 3.5 Å, and the number of residues of the model deposited in the PDB ranged from 133 to 4332. The maximum number of copies in the AU was six, and there were two cases of hetero-oligomers. Also note that each dataset includes one full-length model and one or two single-domain models. For example, in the cases of crystal 5 and crystal 10, there are five predicted models for each crystal, including two full-length models for each unique chain, two single-domain models and one multimer model. Furthermore, these datasets include some more challenging cases, such as a multi-helical structure in crystal 1, an extremely large structure in crystal 2, and multimeric structures in crystal 5 and crystal 10.

Table 1 The 13 crystal structures included in CASP14 and the predicted targets associated with each structure Crystal No. PDB entry Resolution No. of residues in the AU No. of chains/unique chains CASP EUs† Local AlphaFold‡ Residue Reference 1 6poo 3.03 273 1/1 T1030   273 Manne et al. (2020) T1030-D1   154 T1030-D2   119 2 6vr4 3.5 4332 2/1 T1031-D1   95 Drobysheva et al. (2021)           T1033-D1   100             T1035-D1   102             T1037-D1   404             T1039-D1   161             T1040-D1   130             T1041-D1   242             T1042-D1   276             T1043-D1   148               T1044 2180   3 6n64 3.3 1071 6/1 T1032   284 Chen et al. (2020) T1032-D1   170 4 6ya2 2.5 551 3/1 T1038   199 Bahat et al. (2020) T1038-D1   114 T1038-D2   76 5 6px4 1.65 427 4/2 T1046s1   74 Krieger et al. (2020) T1046s1-D1   72 T1046s2   142 T1046s2-D1   140   T1046s1+T1046s2 216 6 6y4f 1.75 134 1/1 T1049   141 Jiang et al. (2020) T1049-D1   134 7 7m7a 3.2 2125 4/1 T1053   580 Hsieh et al. (2021) T1053-D1   405 T1053-D2   171 8 6yj1 2.3 338 2/1 T1056   186 To be published T1056-D1   169 9 7jtl 2.04 203 2/1 T1064   106 Flower et al. (2021) T1064-D1   92 10 7m5f 1.59 217 2/2 T1065s1   127 To be published T1065s1-D1   119 T1065s2   98 T1065s2-D1   98   T1065s1+T1065s2 225 11 7oc9 1.5 133 1/1 T1074   202 Alexander et al. (2021) T1074-D1   132 12 6x6o 1.52 149 2/1 T1082   97 Shi et al. (2020) T1082-D1   75 13 7k7w 1.77 189 1/1 T1090   193 Newman et al. (2020) T1090-D1   191 †EUs in CASP14. The suffixes `-D1' and `-D2' represent that the structure is divided into `domains' from the predicted structure of the full sequence. The suffixes `-s1' and `-s2' signify that the structure is a subunit whose whole structure has two unique chains. ‡Predicted models from local installation of AlphaFold. The sign `+' represents that the structure is predicted by the multimer edition.

2.2. Model prediction

The predicted models were generated by AlphaFold based on the sequence files. The predicted models primarily consisted of three types, including single-domain models, full-length models and multimer models. CASP14 provides both single-domain models, which were decomposed into evaluation units (EUs) and full-length models, along with global distance test total scores (GDT_TS). We selected the predicted model with the highest GDT_TS, as higher values indicate a more accurate backbone and better overall model quality. All models were generated using AlphaFold (group No. 427). For the special case T1044 and multimer models, the corresponding AlphaFold models were not available on the website, so the predictions were performed using the local installation on a workstation of the code distributed via the repository at https://github.com/deepmind/alphafold. For the locally predicted models, we selected the top-ranked models. All predicted models were unmodified. The RMSD of C^α after alignment with the PDB model was calculated.

2.3. Molecular replacement

Molecular replacement was performed by auto mode in Phaser. We tested three scenarios with different search models, including a full-length model, multiple single-domain models and an individual single-domain model. When using a full-length model or individual single-domain model, only one predicted model was used as an ensemble in Phaser. While using multiple single-domain models, multiple predicted single-domain models were employed as ensembles to increase the chances of success in MR. The structures generated by the program were used as the starting point for further model completion, and the translation function Z score (TFZ) was recorded. R factors were calculated using Phenix.Refine (Afonine et al., 2012) and the RMSD of C^α after alignment with the PDB model was calculated and recorded.

In addition, model-map CC validation was also used for model copy screening in some difficult cases to remove the unfitted parts of the MR model. Here, CC is the correlation coefficient between the model and density map, calculated by Phenix.get_cc_mtz_pdb when it is lower than 0.6, this means that there is an unsatisfactory match between the structure and the electron density, and the model can be deleted.

2.4. Phase extension and model completion

Further phase extension and model completion were implemented in the direct-methods-aided dual-space iterative phasing and model-building workflow in IPCAS 2.0. The workflow can be divided into four parts: (1) Reciprocal-space phase refinement by OASIS. The initial model and phases produced by MR and restrained refinement will be delivered to the direct-methods-aided software OASIS for phase refinement and extension. (2) non-crystallographic symmetry (NCS) matrices searching by Phenix.Find_NCS_From_Density (Terwilliger, 2013). If there are more than one copy of the molecule in the AU, multifold operator searching will be performed by Phenix.Find_NCS_ From_Density. If the NCS operator can be found and the correlation coefficient (NCS_CC) of electron density of the related areas is greater than a certain value (0.5 for the first cycle or the largest value during the cycle), the information for the NCS matrices will be recorded. (3) Density modification by DM or Parrot. The electron density map calculated in step (1) will be further modified by DM or Parrot with the NCS information in step (2). A new MTZ file with a set of improved phases and figures of merit (FOM) will be created. (4) Real-space model building and refinement by Buccaneer and Phenix.AutoBuild in alternate mode. Many test cases show that the alternate running of Phenix.AutoBuild and Buccaneer can better prevent the process diverging or converging to one of the local extrema.

The whole procedure can be performed iteratively. During each iterative cycle, NCS matrices are updated sustainably in step (2), and the R factors and the modeled residues are used to monitor the result model, the result from the trial with the most modeled residues or the smallest R factor will be passed on to the next cycle until a satisfactory model is obtained or the maximal running cycles condition has been reached. The whole workflow is shown in Fig. 1.

Figure 1 Flowchart of the combination of structure prediction, MR and direct-methods-aided model completion. Programs involved: MR, Phaser; direct-methods-aided model completion, IPCAS 2.0. Flowchart of the direct-methods-aided model completion in IPCAS 2.0. Programs involved: rigid-body refinement, Refmac; NCS searching, Phenix.Find_NCS_From_Density; direct-methods phasing, OASIS; density modification, DM or Parrot; model building, Phenix.AutoBuild or Buccaneer; final refinement, Phenix.Refine.

By default, 50 cycles of the OASIS–DM/Parrot–Phenix.AutoBuild&Buccaneer iteration are performed, but are stopped halfway when R_free reaches 0.30. The best model will be further improved by Phenix.Refine to obtain the final structure. R factors were calculated using Phenix.Refine, and the RMSD of C^α after alignment with the PDB model was calculated and recorded.

3.1. Results of the full-length models

The full-length predicted models can provide a general idea of the overall structure of unknown proteins, but inevitably there are some significant local deviations, especially in disordered or flexible regions.

In total, 13 out of 15 cases, with the exceptions of crystal 1 (PDB entry 6poo, case 1) and crystal 3 (PDB entry 6n64, case 3), were successfully placed by MR using the AlphaFold full-length models, and could be solved straightforwardly using the default protocol. As illustrated in Fig. 2(a), the MR method resulted in significant phase improvement, with the phase error of most cases reduced from around 90° to 48–79°. When the MR models were delivered to IPCAS, the local deviations and model bias of the structures could be further corrected in the direct-methods-aided model completion protocol. A significant decrease in phase error (−20 to −40°) was exhibited in the initial five cycles in IPCAS. Subsequent cycles, on the other hand, resemble a more refined fine-tuning process towards achieving the final structure. Eventually, IPCAS could build more than 90% of the completeness after 15 cycles of iteration and yield final models for most cases with acceptable refinement statistics (R factor ≤ 0.30, except in cases 1 and 3).

Figure 2 Plots of the mean phase error calculated against the crystal structure at key steps in the process. (a) Results of full-length models (case 3 is unsolved). (b) Results of multiple single-domain models. (c) Results of individual single-domain models (case 23 required 35 cycles of convergence).

Crystals 1 and 3 possess certain structural specificity, making it difficult to find a valid solution by MR starting from the full-length model. Crystal 1 is an multi-helical structure (PDB entry 6poo). The full structure was designated the `multidom' CASP target with two domains. The full-length prediction structure T1030 could not be placed by MR in case 1. Crystal 3 has six copies of the sequence in the AU in three dimers. Although the full-length prediction structure T1032 could be placed by MR in case 3, it resulted in very high R factors (>0.55) which posed a significant challenge for the subsequent model completion.

Also note that two PDB structures, crystal 5 (PDB entry 6px4) and crystal 10 (PDB entry 7m5f), each containing two unique chains, were tested using two different strategies. First, the prediction structures of these two unique chains were used as distinct components in MR, such as cases 5 and 11. Second, the multimer predicted model was treated as one component, such as cases 6 and 12.

3.2. Results of the multiple single-domain models

When the full-length model fails, trimming out unstable parts of the predicted model, such as flexible loops, and performing MR simultaneously on multiple domain models have shown to improve the success rate of MR. Six cases, cases 16–21, have been tested and all of them were successfully solved using the default protocol. As shown in Fig. 2(b), the phase error variation follows a similar pattern to that of the full-length cases. The optimization of phase error primarily occurs during the MR step and the first five cycles of IPCAS iteration. Note that, compared with the full-length models, the average phase error is much lower after the MR step (55.7° versus 65.4°). Eventually, IPCAS is able to reconstruct more than 93% of the completeness after 15 cycles of iteration and generate final models for all cases with acceptable refinement statistics (R factor ≤ 0.30).

Notably, three cases stand out: crystal 1 (PDB entry 6poo, case 16), crystal 2 (PDB entry 6vr4, case 17) and crystal 4 (PDB entry 6ya2, case 18). We failed to solve crystal 1 by MR using the full-length predicted model T1030 in case 1. On the contrary, in case 16, successful MR was achieved using the two domain models, T1030-D1 and T1030-D2. Crystal 2 corresponds to the polymerase structure. In case 17, during MR, only 8 of the 18 targets (9 predicted models with 2 copies each) could be accurately placed. Crystal 4 contains 3 copies of the sequence in the AU and has two domains corresponding to the structures of T1038-D1 and T1038-D2. In case 18, 5 out of 6 targets were accurately placed by MR.

3.3. Results of the individual single-domain model

Using only the single-domain portion as the starting model, a more conservative region can be selected, which effectively reduces the model bias between the predicted model and the ultimate structure, and it helps with the MR search to some extent. However, using a small model as a starting point can result in a significant loss of structural information, which can make it challenging to complete the entire structure. After the single-domain model was located and the NCS was expanded by MR, the missing regions could be further expanded through the direct-methods-aided model completion strategy in IPCAS. In our test cases, all 17 cases from case 22 to case 38 were solved straightforwardly with the default protocol as depicted in Fig. 1. As shown in Fig. 2(c), the phase error variation follows a similar pattern to that of the full-length or multiple single-domain cases. But compared with the above cases, the correction of phase error is much more significant in the last 10 cycles of IPCAS (2.96° versus 0.6° versus 1.3°). In addition, for case 23, the phase error is still far from convergency after 15 cycles of IPCAS optimization. Eventually, IPCAS is able to reconstruct more than 97% of the completeness after 35 cycles of iteration and generate final models for all cases with acceptable refinement statistics (R factor ≤ 0.30).

There are three cases worth mentioning: crystal 3 (PDB entry 6n64, case 24), crystal 4 (PDB entry 6ya2, cases 25 and 26) and crystal 5 (PDB entry 6px4, cases 27 and 28).

Crystal 3 could not be solved using the full-length prediction structure T1032 in case 3 because of the inaccuracies in MR. However, the domain model T1032-D1 could be placed unambiguously in MR in case 24, despite with high R factors. Crystal 4 has three copies and two domains corresponding to T1038-D1 and T1038-D2. In case 25, starting from T1038-D1, the structure could be solved straightforwardly with the default protocol. But when starting for T1038-D2 in case 26, only two of the three targets could be accurately placed by MR and the misaligned model was then deleted by CC validation (CC < 0.6) before model extension. Crystal 5 contains two unique chains and two NCS copies in the AU. Two single-domain predicted models, T1046s1-D1 and T1046s2-D1, corresponding to the smaller and larger subunits, respectively, were used as starting points in cases 27 and 28. In both cases, two copies were placed unambiguously in MR.

3.4. Details of remarkable cases

Crystal 1 is a multi-helical structure, which can cause modulation of the crystal diffraction data, making MR challenging, as well as difficulties in accurately predicting the interhelical angles. Crystal 2 is an extremely large structure, containing 4332 residues in the AU, which causes difficulties in MR and structure prediction. Crystal 3 has six copies, and the medium resolution and high RMSD of the predicted model make the case difficult. Crystal 4 has two domains and crystal 5 has two unique chains, both of them are multimeric structures. Details are given below.

3.4.2. Crystal 2 (targets T1031, T1033, T1035, T1037 and T1039–T1044)

Crystal 2 (PDB entry 6vr4) is the virion-packaged DNA-dependent RNA polymerase of crAss-like phage phi14:2 at 3.5 Å resolution. The AU contains two copies of the monomer related by a non-crystallographic twofold axis, and the entire structure comprises 4332 residues. The full polypeptide sequence is divided into nine separate domains which refer to T1031, T1033, T1035, T1037, T1039, T1040, T1041, T1042 and T1043 in CASP14, with residue numbers ranging from 95 to 404. Out of the nine separate domains, eight were classified as FM and one was classified as FM/TBM. The extremely large structure posed challenges for both structure prediction and MR, while the moderate resolution further increased the difficulty of MR.

In the study by McCoy et al. (2022), the authors claimed that, due to low resolution, a model required for MR had to represent, at least to some extent, the fold of the target protein. Obviously, for this special case, it is not sufficient to build the complete structure from a single target. But even starting from nine separate domains provided by CASP14, only 12 out of 18 monomeric domains could be placed in sequence using NCS relationships and refinement methods. The final structure had an RMSD over 2.5 Å when compared with the PDB structure.

We also performed MR on the multiple domain models in case 17. In automatic mode, Phaser was just able to align 8 out of the 18 copies, including T1031, T1033, T1042 and T1043 from one copy; and T1037 and T1041 from two copies, with a C^α RMSD of 49.8 Å over 3204 residues. As shown in Fig. 3(b), the MR model is far from the final result. But the numerous errors and gaps could be largely corrected using the standard workflow of direct-methods-aided model completion in IPCAS. In the beginning of the third cycle, the missing parts and model bias are rapidly reconstructed and corrected. Additionally, the phase errors tend to converge starting from the fifth cycle. Finally, after a 15 cycle iteration, the errors were essentially rectified, and the gaps improved. The IPCAS structure exhibited excellent parameters with R factors of 0.21 and 0.26, completeness of 93.51%, and an RMSD of 2.4 Å over 4018 residues [as shown in Fig. 3(c)].

Figure 3 Crystal 2 (PDB entry 6vr4), targets T1031, T1033, T1035, T1037 and T1039–T1044. (a) Model from Phaser based on T1031, T1033, T1035, T1037 and T1039–T1043. (b) Model (a) superimposed with the crystal structure. (c) Model from IPCAS based on model (a). (d) Model (c) superimposed with the crystal structure. (e) Model from Phaser based on T1044. (f) Model (e) superimposed with the crystal structure. (g) Model from IPCAS based on model (e). (h) Model (g) superimposed with the crystal structure.

For the full-length prediction of 6vr4, the corresponding AlphaFold models were not available on CASP14, so the prediction was performed using the local installation. The top-ranked model was subjected to the standard procedure in case 2 (as shown in Fig. 1). The resulting final structure showed a significant improvement, with the RMSD reduced from 3.1 Å over 2166 residues to 0.5 Å over 3850 residues. The completeness also increased to 91.27%, and the R factors were 0.22 and 0.27, respectively [as shown in Fig. 3(g)].

3.4.5. Crystal 5 (target T1046)

Crystal 5 (PDB entry 6px4) is the crystal structure of the complex between periplasmic domains of antiholin RI and holin T from T4 phage, in H32. There are two copies of the dimer in the AU related by a non-crystallographic twofold axis, containing 427 residues. This is a typical multimeric structure; therefore, in addition to the three sets of testing schemes mentioned above (full-length, multiple single-domain, single-domain only), we also conducted a structural analysis test on the whole multimer model.

The full polypeptide sequence of antiholin RI and holin T consists of 74 and 142 residues, respectively, which correspond to targets T1046s1 and T1046s2. T1046s1 represents one chain with fewer residues, consisting of three helices. T1046s2 represents the other chain with more residues, consisting of three α-helices and five β-sheets. Each chain has one domain, denoted `-D1', shown as T1046s1, T1046s1-D1, T1046s2 and T1046s2-D1. Since the corresponding AlphaFold multimer model was not available on the website, the prediction was made by a local installation. Compared with the reference structure, the predicted multimer model has accurate distances between subunits, with C^α RMSD values less than 1.2 Å over 214 residues.

After MR, the predicted models were further refined using direct methods to improve the structure details. For all five cases, the final models had R factors no greater than 0.25, completeness greater than 98% and RMSDs less than 0.15 Å. Interestingly, in cases 27 and 28, it was observed that both the larger and the smaller domains of the single-domain models T1046s1-D1 or T1046s2-D1 could be extended to form the complete structure during the IPCAS iteration, as depicted in Fig. 4. Furthermore, in the case of full length and multimer structures (cases 5 and 6), the IPCAS models demonstrated a significant decrease in RMSD values to 0.09 Å, indicating the validity and effectiveness of the improvements made.

Figure 4 Crystal 5 (PDB entry 6px4), target T1046. (a) Model from Phaser based on T1046s1-D1. (b) Model (a) superimposed with the crystal structure. (c) Model from IPCAS based on (a). (d) Model (c) superimposed with the crystal structure. (e) Model from Phaser based on T1046s2-D1. (f) Model (e) superimposed with the crystal structure. (g) Model from IPCAS based on (e). (h) Model (g) superimposed with the crystal structure.

4.1. The characteristics of three kinds of predicted models

The full-length predicted models can provide a general idea of the overall structure of unknown proteins. When target proteins have moderate length (residues number range from 100 to 1000) and relatively conservative structure (RMSD less than 5 Å), the full-length predicted model is an ideal starting structure for MR and model completion, as shown in Table 2.

Starting from the multiple single-domain models indeed has a high success rate and good universality in various test cases. However, the key to success or failure lies in how to divide the domain appropriately. If the domain selection is too strict, it may lead to a reduction in the completeness of the model, which is not conducive to the accurate solution of the MR method. On the other hand, if the domain selection is too loose, it may introduce flexible regions, which will also pose difficulties in the subsequent MR solution. To address this challenge, it is crucial to strike a balance in domain selection. One approach is to carefully analyze the protein structure and consider the structural and functional characteristics of the domains. This analysis can help to identify regions that are likely to be stable and have distinct boundaries, which can be treated as separate domains. It is also important to consider any available experimental data, such as domain annotations or functional studies, to guide the domain selection process. In addition, utilizing computational tools and algorithms specifically designed for domain prediction can be helpful. These tools can analyze the protein sequence and predict potential domain boundaries based on various features, such as secondary structure, solvent accessibility and evolutionary conservation. In our work, we recommend a method that takes inspiration from classification of target EUs in CASP14 to segment the predicted models into domains. Target domains can be defined initially using DomainParser (Xu et al., 2000), DDOMAIN (Zhou et al., 2007) or Sword (Postic et al., 2017) packages. Then, considering the possible differences between the predicted model and the actual crystallized portion, it will be determined whether the domain models in the terminal should be removed because of the flexibility. The remaining compact domain models will be used as the starting point for structure determination.

Compared with the first two kinds of models, the single-domain model can minimize the influence of model bias on structure construction. Therefore, for situations where the data resolution is high or the high-accuracy structure is mandatory, the single-domain model can be preferred as the starting model. However, since a complete protein can be divided into different single domains, how to choose the most suitable one also has the same problems we mentioned above. Fortunately, with the aid of IPCAS, a smaller model can be tolerated as the starting model, which provides more possibilities for single-domain selection (Table 4).

4.2. The characteristics of more challenging cases

According to the results in Tables 2–4, for the more challenging cases, such as multi-helical structures (crystal 1, PDB entry 6poo), multimeric structures (crystal 5, PDB entry 6px4; crystal 10, PDB entry 7m5f) and extremely large structures (crystal 2, PDB entry 6vr4), different characteristics are shown.

For multi-helical structures, this type of structure is the most challenging to solve with the AlphaFold models. The problem is twofold. Firstly, the subtle bends and kinks in the helices are more elusive which have long-range effects in the fit of the model to the target. Secondly, coiled coils induce modulations in the diffraction data which confound the maximum-likelihood targets in MR. These are the reasons for the failure of MR in case 1. These problem can be resolved by decomposing the predicted model into single-domain models, as demonstrated in cases 16, 22 and 23. We recommend the strategy of decomposing the predicted model into multiple single-domain models, as demonstrated in case 16. This approach enhances the likelihood of successful MR and facilitates rapid convergence during subsequent completion in IPCAS.

For multimeric structures, in addition to the accuracy of individual chain structures, the distances between chains need to be considered. Currently, AlphaFold-Multimer is capable of accurately predicting multimeric structures, shown in cases 6 and 12. In our test cases (cases 5, 6, 11, 12, 19, 21, 27, 28, 34 and 35), the success of MR and the subsequent rapid convergence during model completion in IPCAS were achieved regardless of the strategy employed. This also highlights the universality of our program and strategy. For this type of structure, the strategy with any available predicted model could be applied.

For extremely large structures, structure prediction can be challenging in terms of length and accuracy. On one hand, predicting protein structures with over 1000 amino acids requires high hardware specifications. On the other hand, local deviations in predicted models can impact the overall structure, especially for extremely large structures. For this type of structure, the strategy of predicting single-domain models in segments is recommended, as demonstrated in case 17. In comparison with case 2, although there were misplacements of single-domain models in the MR process of case 17, model completion through IPCAS using direct methods was able to correct the biases introduced by the MR model.

4.3. Contribution of IPCAS in phase optimization and structure completeness

Regardless of the prediction structures used as the starting point for MR, there are often deviations or incompleteness between the MR models and the reference structures. In our study, we employed direct-methods-aided model completion in IPCAS to correct and extend the predicted model after MR. An important characteristic of IPCAS 2.0 is its incorporation of direct methods (Fan & Gu, 1985b) into the phasing and model-building dual-space iteration, a resolution-screening method for NCS searching and an alternate model-building protocol.

The direct-methods program OASIS plays a crucial role by performing a 180° phase flip of inaccurate phases in reciprocal space. Numerous publications have demonstrated the suitability of this pipeline for phase refinement and optimization of low-resolution diffraction data, even at resolutions as low as 5 Å (Fan et al., 1998, 2014; Wu et al., 2009; Yao et al., 2014; Ding et al., 2020). In our study, we tested 38 cases, and only two were unresolved due to the failure of MR. Among the remaining cases, 34 achieved phase optimization within the first five cycles of iteration, followed by structural refinement in the subsequent ten cycles. For two special cases, 22 and 23, direct-methods phase optimization required iterations until the 11th and 30th cycles, respectively, to achieve significant results. Furthermore, to demonstrate the effectiveness of OASIS, we tested the iteration with and without OASIS for the most challenging cases using the individual single-domain predicted model as the starting point, as presented in Fig. 5. It is evident that cases 22 and 23 were unable to be resolved successfully without the aid of OASIS. The iterations without OASIS failed directly and were completely destroyed within a few cycles, resulting in a set of atoms without any secondary structure, as shown in Figs. 6(a) and 6(b). Figs. 6(c) and 6(d) also show that the phase error of the iterations with the direct-methods program OASIS gradually decreases, whereas the iterations without OASIS lead to an increasing phase discrepancy, further highlighting its significance.

Figure 5 Comparison of iterative results with and without OASIS. (a) Comparison of Rwork. (b) Comparison of Rfree. (c) Comparison of RMSD. (d) Comparison of completeness.

Figure 6 Model completion of the N-terminal helical domain of BibA with the MR model. (a) Model completion with the T1030-D1 MR model. Upper row, models from 15 cycles of OASIS–Parrot–Phenix.AutoBuild&Buccaneer iteration; lower row, models from 15 cycles of the Parrot–Phenix.AutoBuild&Buccaneer iteration (bypassing OASIS in the flowchart in Fig. 1). The starting models and reference PDB structures are shown on the left and right, respectively. (b) Model completion with the T1030-D2 MR model. Upper row, models from 35 cycles of the OASIS–Parrot–Phenix.AutoBuild&­Buccaneer iteration; lower row, models from 35 cycles of the Parrot–Phenix.AutoBuild&Buccaneer iteration (bypassing OASIS in the flowchart in Fig. 1). The starting models and reference PDB structures are shown on the left and right, respectively. (c) Variation of phase error during model completion of the N-terminal helical domain of BibA with the T1030-D1 MR model. (d) Variation of phase error during model completion of the N-terminal helical domain of BibA with the T1030-D2 MR model.

Moreover, the resolution screening method for non-crystallographic symmetry searching also works well in the cases with NCS copies, particularly in cases where the MR method fails to accurately determine the correct position of all models (e.g. case 26). In addition, by implementing an alternate model-building method (such as Phenix.AutoBuild and Buccaneer) the premature convergence of the iterative partial-structure extension process can be effectively avoided. As shown in case 31, the phase error rapidly decreases to a range approaching convergence, after two significant increases in the alternate model-building cycle.

4.4. RMSD analysis of the IPCAS models and the predicted models

The RMSD analysis of the predicted models and the final structures obtained through the protocol is shown in Fig. 7. For the predicted sequence regions, the RMSD of the IPCAS model is consistently lower than the predicted model for all cases. This indicates that our process is capable of effectively correcting biases in predicted models, aided by the diffraction data.

Figure 7 Comparison of the IPCAS models with the predicted models in RMSD. The RMSD values were calculated by comparison with the corresponding target PDB structures. The sequence regions evaluated by the IPCAS models align with the predicted models for assessment.

4.5. Correction of the excess portions of the predicted models

In the Results, particularly in Section 3.1, we observed that some of the MR models exhibit completeness greater than 100%. This phenomenon can be attributed to variations in the size of the predicted models compared with the actual regions crystallized. In such cases, it is necessary to correct the excess portions of the predicted models. For instance, in case 13, an additional section of a random loop consisting of approximately 65 residues was present at the N-terminal of the predicted model, leading to a model completeness of 151.9%. Through the direct-methods-aided model completion, the majority of the random coil region can be automatically removed. As a result, the final model obtained contains one residue more than the corresponding model in the PDB. Further details regarding this process can be found in Fig. 8.

Figure 8 Crystal 11 (PDB entry 7oc9), target T1074. (a) Model from Phaser based on T1074. (b) Model (a) superimposed with the crystal structure. (c) Model from IPCAS based on (a). (d) Model (c) superimposed with the crystal structure. (e) The 2Fo − Fc electron density map at a contour level of 1.1σ, with a focus on the N-terminal helix region.

In cases where the completeness of the final models exceeds 100%, there are two possible scenarios. Firstly, as previously discussed, it is possible that the predicted models are larger than the actual models, causing the inclusion of poorly density-resolved residues during the model completion process. Secondly, in certain cases, the modeling process involves extending partial structures to complete structures while preserving flexible regions, which lead to a final completeness greater than 100%. These flexible regions may be removed during subsequent inspection of the PDB model. This scenario can be observed in case 30.

4.6. The refinement and model-building process for the molecular replacement model

Once the initial models are obtained through MR, the subsequent critical steps involve refinement and model building, typically performed using software like Phenix (Phenix.AutoBuild) and CCP4 (Buccaneer). Table S1 and Fig. S1 of the supporting information present the statistical results of modeling and refinement for the MR models, using Phenix (Phenix.AutoBuild), CCP4 (Buccaneer) and IPCAS. Among the 38 cases, using an R_work/R_free threshold of less than 0.30, there are 36 IPCAS models, 13 AutoBuild models and 8 Buccaneer models. If the R_free threshold is relaxed to 0.35, there are 36 IPCAS models, 21 AutoBuild models and 16 Buccaneer models [Figs. S1(a) and S1(b)]. Similar results can also be found in the curve of RMSD and completeness [Figs. S1(c) and S1(d)]. This fully demonstrates that when the initial model proves to be sufficiently accurate, it allows for the automatic generation of a nearly complete model without further manual intervention. And for the more challenging cases, such as multi-helical structures (crystal 1, PDB entry 6poo, cases 16, 22 and 23), multimeric structures (crystal 5, PDB entry 6px4, cases 5, 6, 19, 27 and 28; crystal 10, PDB entry 7m5f, cases 11, 12, 21, 34 and 35) and extremely large structures (crystal 2, PDB entry 6vr4, cases 2 and 17), IPCAS consistently produced the final structure, whereas only partial cases were resolved using Phenix.AutoBuild or Buccaneer.

In summary, the combination of structure prediction with MR, model building and refinement is an effective approach for biomacromolecular structure determination. And as for the IPCAS pipeline, the strategy is advantageous with the direct methods P₊ formula for phase optimization and alternating between Phenix.AutoBuild and Buccaneer for model building to avoid local extrema, which can effectively improve the success rate of challenging cases.